Can anyone help me to break this long formula on two lines?

%PSI ( r,%theta,%phi ) =N lbrace sqrt2 %psi_{2,1,-1} (r,%theta,%phi) - sqrt3 %psi_3,1,1 (r,%theta,%phi)

-sqrt5 %psi_2,1,1 (r,%theta,%phi) + sqrt6 %psi_3,1,0 (r,%theta,%phi) rbrace

this formula needs to be broken down in two lines. I tried the newline, left none , right none all these commands. But they do not seem to work inside lbrace and rbrace. can anyone help me with this please ?

You need to use left lbrace instead of simple lbrace; right rbrace instead of rbrace. Then those right none newline left none inserted in the newline would do their job.

%PSI ( r,%theta,%phi ) =N left lbrace sqrt2 %psi_{2,1,-1} (r,%theta,%phi) - sqrt3 %psi_3,1,1 (r,%theta,%phi) 
right none newline left none
-sqrt5 %psi_2,1,1 (r,%theta,%phi) + sqrt6 %psi_3,1,0 (r,%theta,%phi) right rbrace

If you want alignment, this might be an alternative:

matrix {
alignr %PSI ( r,%theta,%phi )#{} ={} # alignl N left lbrace sqrt2 %psi_{2,1,-1} (r,%theta,%phi) - sqrt3 %psi_3,1,1 (r,%theta,%phi) right none ##
alignr {} # {} {} # alignl left none -sqrt5 %psi_2,1,1 (r,%theta,%phi) + sqrt6 %psi_3,1,0 (r,%theta,%phi) right rbrace

}

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It’s not pretty, but you could replace the braces with escaped characters:

%PSI ( r,%theta,%phi ) =N \{ sqrt2 %psi_{2,1,-1} (r,%theta,%phi) - sqrt3 %psi_3,1,1 (r,%theta,%phi) 
newline 
-sqrt5 %psi_2,1,1 (r,%theta,%phi) + sqrt6 %psi_3,1,0 (r,%theta,%phi) \}